ИСТИНА

The conditions for the loss of stability and the character of the loss of stability of the system described by the equation with integral operator with aftereffect are investigated. Such dynamic system is the model of transverse oscillations of a pipeline with a uniformly flowing fluid, taking into account the inertia forces of the pipe and liquid, the moments of Coriolis forces and centrifugal forces, and the Kelvin-Voigt friction. Both ends of the pipeline are fixed in a hinged manner, and the elastic characteristics are constant. It is shown that as the velocity of the fluid increases, the system loses stability, and the nature of the loss of stability is divergent. The presence of points of accumulation of the spectrum indicates the lack of controllability by a control function, concentrated on one of the bounds.